Question

Which of the following relations is a function ?
A. (2,4),(-4,6),(2,3),(-7,2) B. (2,4),(-4,2),(7,1),(-7,2) C. (2,0),(-4,3),(7,1),(-4,5) D. (7,1),(-4,4),(2,1),(7,2)

Answer 1

All right let's start with A.
In order for the relation to be a function, none of the numbers in the domain (the second number in each pair) can be the same. Tell me, in choice A are any of the numbers in the domain the same @AniyahM17?

Answer 2

Put it slightly differently, a function's value (the y-value) should be unique for a given value of in the domain (x-value).
If all the x-values in the domain are different, the relation is definitely a function. If both x- \(and\) y-values repeat, the relation is still a function, because it is simply a repetition of the points.
However, if the x-value repeats but with a different y-value, then the relation is NOT a function because we do not have a unique y-value (range) for a given x-value (domain).
Examples:
(1,4),(2,5),(3,6) - x-values {1,2,3} do not repeat, so a functions
(1,2),(2,3),(3,4),(1,3) - 2 x values equal to 1, and corresponding y-values are {2, 3}, so there is no unique y-value for x=2, the relation is NOT a function.
(1,2),(2,3),(3,4),(1,2) - (1,2) appears twice, that makes just a repetition, one of them can be taken out, so it is a function.

As suggested by @AMYCARTER , examine each relation carefully.
If all the x's are different, the relation is a function.
If some x's repeat, check the y. If the two points are identical, remove the second point, and continue checking. If you find two different points have the same x, then the relation is not a function.